In a message dated 97-09-21 17:50:02 EDT,mark snyder wrote
<< what that means is that e^x has no meaning if x has a dimension. This comes from the power series for e^x: it has all powers of x in it, so if x has dimensions of, say, feet, then e^x would have to have dimensions of ft +ft^2+ft^3+..., which is clearly nonsensical (you can't add a length to an area and get something which corresponds to any physical quantity: what would be its dimension?). >>
Mark, I beg to differ. In the power series x has all the powers as you say, but the coefficients have the various derivatives which have their own units. These should cancel the "extra" units of the powers of x. For example
s(x) in feet as a function of time in seconds s'(x) in ft / sec times (x^1 sec) = feet s''(x) in ft / sec/sec times (x^2 sec^2) = feet s'''(x) in ft sec/ sec/ sec times (x^3 sec^3)= feet etc.